Kane, 32, won and scored a penalty before sealing victory in the second half through a curled shot after a Malo Gusto mistake.

Earlier, Chelsea defender Trevoh Chalobah scored an own goal, while a returning Cole Palmer placed a shot into the top corner to pull one back on his 100th appearance in all competitions for the west Londoners.

There were warnings in the second half as Michael Olise and Kane missed good chances when Chelsea - back in the Champions League for the first time since the 2022-23 season - were chasing an equaliser.

Ultimately, Gusto's misplaced pass led to Kane's curled shot in the 63rd minute that ended the match as a contest.

It was one of a number of defensive mistakes, including the visitors switching off at a drop-ball situation before Chalobah's own goal and midfielder Moises Caicedo bringing Kane down in the box.

Chelsea squandered a positive start, missing early chances through Pedro Neto and Enzo Fernandez, and Palmer also had a late goal ruled out for a narrow offside.

The Blues were ultimately out-thought by a more streetwise and experienced Bayern side, who have won their opening Champions League match for the 22nd season in a row.

Bayern goalkeeper Manuel Neuer, 39, played his 151st match in the Champions League. By contrast, Chelsea's entire 24-man squad had made only 117 appearances at this level before kick-off.

Striker Nicolas Jackson, who joined Bayern on loan from Chelsea on deadline day, was introduced from the bench in the 91st minute without much chance to prove a point to his parent club.

The west Londoners next welcome Benfica in the Champions League, which could see Jose Mourinho return to Stamford Bridge, with the Portuguese expected to be appointed manager this week.

Chelsea analysis: Blues weren't terrible but must learn

Chelsea must learn lessons from this performance at the Allianz Arena.

They were equals to Bayern in the first half but were a goal down after two mistakes despite brilliance from Palmer.

Bayern manager Vincent Kompany made tweaks at the interval, having no doubt spotted Enzo Maresca tried to repeat his tactics from the Club World Cup final win over Paris St-Germain, and the game swung back in the German side's favour.

Kane scored an all-important third goal in the 63rd minute, but multiple chances before then were a signal Maresca should have used his substantial bench sooner.

Estevao Willian, Alejandro Garnacho, Jamie Gittens and a host of other attackers may have swung the game.

Garnacho and Andrey Santos came on immediately after Kane's second goal but it was too late. Estevao also came on and set up Palmer's 88th-minute goal, which was ruled out by a narrow offside call after a VAR check.

Meanwhile, Bayern had only five senior players on their bench. They went down to their fourth-choice option at left-back after an injury to Josip Stanisic early in the second half.

It must also be said that this was far from a disastrous performance and many Chelsea players showed an aptitude to play at this level. Of course, no-one more so than Palmer.

When asked about the lapses, Maresca said: "In this kind of competition, I guess this team required to be full focus and play right away for 95 minutes. I think we played well, but not for the entire game.

"Personally I'm happy with the performance, because we knew how difficult it was to come here against this team. We knew that it was a very tough game, a difficult game. It's a game that we can learn a lot and build something special from this defeat."

Bayern analysis: Kane and Olise unstoppable

Kane is entering into Bayern folklore with his sensational attacking statistics.

The England captain has 10 goals in six matches in all competitions at the beginning of the new season.

It has taken him to a staggering 95 goals in 102 games since moving to the Bavarian club, with a further 29 assists also to his name.

Before kick-off, much of the debate in the German media was also around a change in his game.

Kane has increasingly dropped into deeper positions to play in faster runners from wide positions, adding another string to his bow. Of course, it's a role Kane has often performed with both his former club Tottenham and England.

When asked about Kane's performance, Kompany said: "Every time the question comes about Harry I don't have much to say about what people can see.

"It is more about his work off the ball. Watch him move, press and help the team. He has to run, get back onside to win the penalty. He spends energy to get chances and rewards.

"That's the side of it I keep highlighting. You can talk about quality and talent but there is a lot of hard work behind it."

Kane, along with ex-Crystal Palace winger Olise, have shown themselves capable of leading this club to glory in Europe. (BBC)